class: center, middle, inverse, title-slide .title[ # The impact of COVID-19 vaccines on the Case Fatality Rate: The importance of monitoring breakthrough infections ] .subtitle[ ## April 9, 2022 PAA Annual Meeting ] .author[ ### Vanessa di Lego
1
Miguel Sánchez-Romero
1
2
Alexia Prskawetz
1
2
3
] .institute[ ### 1 Wittgenstein Centre (IIASA, OeAW, University of Vienna)
Vienna Institute of Demography at the Austrian Academy of Sciences
2 International Institute for Applied Systems Analysis, Laxenburg, Austria
3 Institute of Statistics and Mathematical Methods in Economics, Research Unit Economics, TU Wien ] --- class: center, middle # Motivation --- class: middle Fig. 1 Case Fatality Rate (CFR) and %Fully Vaccinated Trajectories <div class="container"> <img class="under" src="data:image/png;base64,#C:/Users/vdile/Documents/Git/CFR_present/img/vax_change.gif"/> <img class="over" src="data:image/png;base64,#C:/Users/vdile/Documents/Git/CFR_present/img/cfr_change.gif"/> </div> .remark-slide-content3[Source: Our World in Data (Mathieu et al. 2021)] --- Fig. 1 Case Fatality Rate (CFR) and %Fully Vaccinated Trajectories <img src="data:image/png;base64,#img/cfr_all_paa.png" width="95%" style="display: block; margin: auto;" /> .remark-slide-content3[Source: Our World in Data (Mathieu et al. 2021)] --- class: Fig. 2 Panel (A) %Case-Fatality Rate (CFR); Panel (B) Share of fully vaccinated persons (%). Austria, by age, from Jan to Dec 2021 <img src="data:image/png;base64,#img/fig2.png" width="95%" style="display: block; margin: auto;" /> .remark-slide-content3[Source: The number of people vaccinated at each group is taken from BMSGPK, Österreichisches COVID-19 Open Data Informationsportal (2021)] --- <img src="data:image/png;base64,#img/vaccine.png" width="50%" style="display: block; margin: auto 0 auto auto;" /> # What is driving this pattern in the CFR? ## Are vaccines not being effective in reducing deaths? --- class: inverse, center, middle # The Sensitivity of the Case-Fatality Rate (CFR) as an Indicator --- class:remark-slide-content ## The CFR is particularly sensitive to <sup>1</sup>: .pull-left-1[ - demographic factors - delays in reported cases - testing policies ] -- .pull-right-2[.content-box-blue[ `$${CFR}_{t,a}=\frac{\text{Deaths}_{t,a}}{\text{Reported Cases}_{t,a}}$$` #### .red[Any] factor that impacts the number of .red[confirmed deaths] from a disease and the number of .red[reported cases] in a given time ### ]] .footnote[[1] (Dowd et al. 2020; Rajgor et al. 2020; Goldstein and Lee 2020; Green et al. 2020; Harman et al. 2021; Smith 2021; Luo et al. 2021; Undurraga et al. 2021)] --- class: inverse, center, middle # The CFR in the presence of Vaccines --- class: middle, center, remark-slide-content .content-box-blue[ `$${CFR}_{t,a}=\frac{\mathcal{D}^{U}_{t,a}+\mathcal{D}^{V}_{t,a}}{d^{U}_{t,a}\mathcal{I}^{U}_{t,a}+\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}$$` ] -- .content-box-blue[ `$$\text{CFR}_{t,a}=\text{CFR}^{U}_{t,a}(1-\color{red}{\gamma_{t,a}})+\text{CFR}^{V}_{t,a}\color{red}{\gamma_{t,a}}$$`] -- `\(\text{CFR}_{t,a}\)` being the weighted sum of `\(\text{CFR}^{U}_{t,a}\)` and `\(\text{CFR}^{V}_{t,a}\)` with weights `\(\color{red}{\gamma_{t,a}}\)`: .pull-left-1[.content-box-red[ `$$\gamma_{t,a}= \frac{\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}{{d^{U}_{t,a}\mathcal{I}^{U}_{t,a}+\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}}$$`]] -- .pull-right-2[ the ratio between the total number of COVID vaccine .red[breakthroughs] and the total number of COVID-associated ever infected and detected cases] --- class: inverse, center, middle, remark-slide-content .content-box-blue[ `$$\text{CFR}_{t,a}=\text{CFR}^{U}_{t,a}(1-\color{red}{\gamma_{t,a}})+\text{CFR}^{V}_{t,a}\color{red}{\gamma_{t,a}}$$`] -- .pull-left-1[.content-box-red[ `$$\gamma_{t,a}= 0$$` ]] -- .pull-right-1[ No .red[breakthrough] cases: `\(\text{CFR}_{t,a} = \text{CFR}^{U}_{t,a}\)`] -- .pull-left-1[.content-box-red[ `$$\gamma_{t,a}\neq0$$` ]] -- .pull-right-1[ How does `\(\text{CFR}^{V}_{t,a}\gamma_{t,a}\)` affect the `\(\text{CFR}_{t,a}\)`?] --- .pull-left-2[.content-box-blue[ `$$\text{CFR}^{V}_{t,a}=\text{CFR}^{U}_{t,a}\frac{(1-\color{red}{\beta_{a}})}{\color{red}{Z_{t,a}}}$$`]] -- .pull-right-1[ `\(\beta_{a}\)` = effectiveness of vaccines in preventing deaths `\(Z_{t,a}\)` = ratio of detection rates between the vaccinated and the unvaccinated if `\(Z_{t,a}=1\)`, the rate of detection among vaccinated and unvaccinated is the same] -- .pull-left-2[.content-box-red[ `$$(1 − \beta_{a} ) = Z_{t,a}$$` the CFR will remain **unchanged**, regardless the fact that the case fatality rate of the vaccinated is **lower** than the case fatality rate of the unvaccinated. ]] -- .pull-left-2[.content-box-purple[the **lower** `\(\beta_{a}\)`, the **higher** `\(Z_{t,a}\)` to keep CFR **constant**. the **higher** `\(\beta_{a}\)`, the **lower** `\(Z_{t,a}\)` to keep CFR constant ]] .footnote[[2] Sánchez-Romero et al. 2021] --- We illustrate the effect CFR scenarios that result from a different combination of `\(\beta_{a}\)` and `\(Z_{t,a}\)` values. - Focus on the 84+, that has the highest risk of dying and was the first vaccinated. - Use Austria as case study for which we have detailed data on deaths, infections, vaccination status and testing by age; Consistent and unique testing policy. - vaccine effectiveness in reducing deaths for ages above 84 is set at 0.85<sup>3</sup> .footnote[[3] Hall et al. 2021] --- class: center, middle # Results --- .remark-slide-content2[Figure 3. Evolution of the %CFR for the age group 84+ in Austria (Jan-Dec 2021) by three different parameter values of] `\(\beta_{(84+)}\)` .remark-slide-content2[and] `\(Z_{(t,84+)}\)` <img src="data:image/png;base64,#img/sim_adj.png" width="90%" style="display: block; margin: auto;" /> .remark-slide-content3[Source: Simulated CFR values are calculated using data from (Richter et al. 2020b, a)and BMSGPK, COVID-19 Open Data Informationsportal (2021)] --- class: middle # Discussion - CFR decline may **not** imply that vaccines are being effective in reducing deaths -- - A constant CFR can **still** mean that vaccines are effective in reducing deaths -- - Detecting infections among both the vaccinated and unvaccinated population is key -- ## Take-away: unless vaccinated people are **also** tested, it is hard to use the CFR as an indicator for monitoring the pandemic --- class: inverse, center, middle Fig. 4 Financial Times Graph on the CFR in Hong Kong: What is the CFR telling us? <img src="data:image/png;base64,#img/Ft_HK.png" width="100%" style="display: block; margin: auto;" /> --- class: Thank you! <img src="data:image/png;base64,#img/simple_wrong.jpg" width="90%" style="display: block; margin: auto;" />